Digital receiver device based on an input comparator

ABSTRACT

A digital processing device is at the input of a radio frequency receiver chain, suited to a transmission system using a direct sequence spectrum spread, comprising analog-to-digital conversion means (ADC) performing an undersampling of a signal received, resulting in an overlapping of the wanted signal by the transmission channel noise, demodulation means connected to the output of the ADC, a low pass filter connected at the output of the demodulation means and a filter matched to the spreading code used, wherein the ADC includes a comparator capable of comparing the amplitude of the undersampled signal to a reference in order to carry out a quantizing of the 1-bit signal, said comparator bringing about the creation of a quantizing noise, and including an additional filtering unit arranged between the low pass filter and the matched filter, implementing a multi-noise, stochastic matched filtering operation.

PRIORITY CLAIM

This application claims priority from French patent application Nos.0504591, filed May 4, 2005, 0504589 filed May 4, 2005, and 0504588,filed May 4, 2005, which are incorporated herein by reference.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is related to U.S. patent application Ser. No.11/429,452 entitled DIGITAL RECEIVER DEVICE and Ser. No. 11/429,392entitled RECEIVER DEVICE SUITED TO A TRANSMISSION SYSTEM USING A DIRECTSEQUENCE SPREAD SPECTRUM which have a common filing date and owner andwhich are incorporated by reference.

TECHNICAL FIELD

In a general way, an embodiment of the invention relates to theprocessing of digital signals and, in particular, to the techniques fordecoding such signals. More specifically, an embodiment of the inventionrelates to a digital processing device that is arranged at the input ofa radio frequency receiver chain and that is particularly suited to atransmission system using a direct sequence spread spectrum,conventionally implemented using phase modulation of the BPSK type (for“Binary Phase Shift Keying”).

BACKGROUND

In a system for transmitting a digital signal using a direct sequencespread spectrum, the “0” and “1” bits are encoded with respectivesymbols sent by the transmitter, and decoded at the receiver by a finiteimpulse response filter.

In the case where the bits are encoded using a spreading code of lengthN, the symbols encoding the “0” and “1” bits are each in the form of aseries of N symbol elements distributed over either of two differentlevels and transmitted at a predetermined fixed frequency F.

The N symbol elements encoding the “1” bit are anti-correlated to thecorresponding N symbol elements encoding the “0” bit, i.e., the symbolelements of the same rank within both of these two symbols have oppositevalues.

For example, if and when a symbol element of the symbol encoding the “1”bit is at level 1, the corresponding symbol element of the symbolencoding the “0” bit is at level −1. In the same way, if and when asymbol element of the symbol encoding the “1” bit is at level −1, thecorresponding symbol element of the symbol encoding the “0” bit is atlevel 1.

The development of digital radio frequency (RF) communications, togetherwith the expansion of mobile telephony, in particular, often demands theuse of multi-standard, very low consumption RF receiver chains. To reachthese objectives, an attempt has been made to reduce to a minimum thedifficult-to-program, analog RF circuitry, by bringing theanalog-to-digital converter (ADC) as close as possible to the receivingantenna. This is then referred to as a “digital/digital/digital”receiver chain.

However, a solution such as this may have the effect of increasing theoperating frequency of the ADC in an unreasonable manner. As a matter offact, given the frequency of the signals involved in radio frequencycommunications, and taking into account the Shannon-Nyquist Theorem(sampling frequency equal to at least twice the maximum frequency of thesignal being sampled), an operation such as this would necessitate theuse of an ADC whose operating frequency would be on the order of severalgigahertz, which is currently commercially impractical.

For this reason, it is conventionally impractical to process the signaldigitally from the moment of reception. Nevertheless, this problem maybe solved by undersampling the digital input signal. This technique,known by the name of undersampling, is based on the principle ofspectrum overlapping and comprises sampling the signal received, not onthe basis of the Shannon Theorem, but at a frequency greater than twicethe signal bandwidth. This is typically valid only if the signal inquestion is a narrowband signal, i.e., if the bandwidth to carrierfrequency ratio is significantly lower than one. Such being the case,the signals involved in the context of RF communications may beconsidered as such. As a matter of fact, their carrier frequency istypically on the order of 2.45 GHz for a bandwidth of a few MHz. Withinthis context of narrowband signals, in which an embodiment of theinvention is situated, it becomes possible, according to theundersampling theory, to sample the signals at a rate much lower thanthat suggested by the Shannon Theorem and, more precisely as explainedabove, at a sampling frequency that depends only on the bandwidth of thenarrowband signal.

In order to illustrate the foregoing, FIG. 1 is a schematicrepresentation of a signal receiving and processing chain, wherein thesignal is captured by an antenna 10, then amplified by a circuit 20referred to as LNA (for “Low Noise Amplifier”) prior to being submittedto the digital signal processing unit 30, referred to as DSP (for“Digital Signal Processing”). The output of the DSP unit may beprocessed conventionally by a processing unit 40, referred to as a CPU(for “Central Processing Unit”).

FIG. 2 is a schematic representation of the various functional unitsinvolved in the conventional digital solution of the DSP unit 30 of FIG.1, which implements undersampling.

The DSP unit includes an analog-to-digital converter 31. The signalbeing a narrowband signal, the sampling frequency Fe is not selectedaccording to the Shannon-Nyquist Theorem, but according to theundersampling theory. Therefore, Fe is determined irrespectively of themodulation carrier frequency. In fact, it is assumed to be equal to atleast twice the bandwidth of the binary message after spread spectrum.For example, for a bandwidth of 2 B, the sampling frequency Fe is givenby Fe≧4 B. Furthermore, the analog-to-digital converter conventionallyuses an M-bit binary representation of the samples, linearly translatingthe sampled analog values contained between two signal levels into 2^(M)digital codes.

The ADC is followed by a stage 32 for estimating the new carrierfrequency fp, designating the new center frequency of the signal afterundersampling, and by the phase φ corresponding to the carrier phase.The estimation stage will likewise make it possible to determine theminimum number of samples necessary for describing a bit time (Tb),i.e., the time to transmit one bit of the spread message, which depends,in particular, on the length of the spreading code used.

According to the undersampling theory, the carrier frequency of thesignal is modified and assumes the following as a new value:

${fp} = {{fm} - {k\frac{Fe}{2}}}$where fm represents the initial carrier frequency and where k designatesa parameter of the undersampling given by:

$k < \frac{{fm} - B}{2B}$

The phase shaft after undersampling is estimated by using a phaseestimator.

The signal present at the output of the estimation stage will befiltered by a band-pass type filter 33, so as to retain only the basemotif of the undersampled signal. As a matter of fact, since thespectrum of the undersampled signal comprises a multiplicity of spectralmotifs representative of the message, a pass-band filtering operation iscarried out in order to retain only a single spectral motif. Therefore,the characteristics of this pass-band filter are as follows:

-   -   Center frequency: fp    -   Bandwidth: 4 B

The filter 33 may include either an infinite or finite impulse responsefilter (IIR, FIR).

The signal is subsequently brought back to baseband by demodulationmeans 34. The undersampled message being conveyed to the carrierfrequency fp, this demodulation step comprises a simple multiplicationstep using a frequency fp of phase φ sinusoid, these two characteristicquantities coming from the estimation stage.

A low pass filtering stage 35 at the output of the demodulation stagemakes it possible to eliminate the harmonic distortion due to spectralredundancy during demodulation of the signal. As a matter of fact, thedemodulation operation reveals the spectral motif of the baseband signalbut also a spectral motif at twice the demodulation frequency, i.e., atabout the frequency 2 fp.

A matched filter stage 36 corresponding to the code of the wanted signalmakes it possible to recover the synchronization of the signal beingdecoded with respect to the wanted information. More precisely, this isa finite impulse response filter, characterized by its impulse responsecoefficients {a_(i)}_(i−0,1, . . . n).

Its structure, described in FIG. 3, is that of a shift register REGreceiving each sample of the input signal IN. The shift registerincludes N bistable circuits in the case of symbols with N symbolelements, which cooperate with a combinational circuit COMB, designed ina manner known by those skilled in the art and involving the series ofcoefficients a_(i) such that the output signal OUT produced by thefilter has an amplitude directly dependent upon the level of correlationobserved between the sequence of the N last samples captured by thisfilter and the series of the N symbol elements of one of the twosymbols, e.g., the series of the N elements of the symbol encoding a “1”bit of the digital signal.

Thus, the matched filtering operation comprises matching the series ofcoefficients a_(i) to the exact replica of the selected spreading code,in order to correlate the levels of the symbol elements that it receivesin succession at its input to the levels of the successive symbolelements of one of the two symbols encoding the “0” and “1” bits, e.g.,the symbol elements of the symbol encoding the “1” bit.

The output signal from the finite impulse response filter 36 can then bedelivered to a comparator, not shown, capable of comparing the amplitudeof this output signal to a lower threshold value and to an upperthreshold value, in order to generate a piece of binary information. Thecomparator is thus equipped to deliver, as a digital output signalrepresentative of a decoded symbol of the input signal, a first bit,e.g., “1”, when the amplitude of the output signal of the filter 36 ishigher than the upper threshold value, and a second bit, e.g., “0”, whenthe amplitude of the output signal of the additional filter is lowerthan the lower threshold value.

However, the conventional undersampling chain such as the one justdescribed, upon which the digital processing of the signal from themoment of its reception relies, may experience serious malfunctions oncethe noise power in the transmission channel becomes elevated. This mayresult in a degradation of the signal-to-noise ratio after processing,primarily when the interfering signal, corresponding to the noise of thetransmission channel, cannot be considered a narrowband signal.

As a matter of fact, as a result of the undersampling, the so-calledspectrum overlap phenomenon is conventionally observed wherein all ofthe frequencies higher than half the sampling frequency are “folded”over the baseband, causing a potentially unacceptable increase in thenoise power in the signal being processed. This may result in anunacceptable error rate at the output of the decoding process.

This signal-to-noise degradation phenomenon in the transmission channel,amplified by the undersampling technique employed, is the principalreason for which the reception solutions based ondigital/digital/digital receiver chains are at present dismissed,despite the undeniable advantages that they might obtain in terms ofprogramming and consumption, in particular.

In order to attempt to improve this signal-to-noise ratio degraded afterprocessing, various solutions might be attempted, short of beingsatisfactory. In particular, it might be anticipated to increase thepower of the signal upon transmission, which, however, involves aconsequential increase in the electrical power consumed by the circuit.It might also be anticipated to use larger spectrum-spreading codes, butthis may be detrimental to the speed, which would thereby be greatlyreduced.

Furthermore, another disadvantage of the undersampling chain of theprior art is due to the use of the analog-to-digital converter.

As a matter of fact, in order to optimize the analog-to-digitalconversion of the signal received, the processing chain makes use of anM-bit resolution ADC, wherein, for example, M=4, which makes it possibleto replace the exact analog value of the sample with the closestpossible approximate value extracted from a finite set of 2^(M) discretevalues. The approximation obtained is therefore better to the extentthat the ADC resolution is greater. There is interest then in limitingthe additive quantizing noise, which corresponds to the gap between thequantizing value attributed to the sample and the exact value of thesample.

That being said, the use of an M-bit ADC likewise leads to the use ofM-bit digital filter and digital multiplier structures for the remainderof the processing and, in particular for the digital bandpass filteringoperation. Thus, out of concern for limiting the quantization noise, theuse of an M-bit ADC may end up being disadvantageous, on the one hand,with respect to the electric power consumed and, on the other hand, withrespect to the surface area occupied by the digital receiver chain whenit is implemented in an integrated circuit.

SUMMARY

An embodiment of the invention eliminates the above-describeddisadvantages by proposing an improved digital/digital/digital receiverdevice, based on a particular analog-to-digital input conversionstructure, enabling an appreciable gain with respect to theimplementation surface area and power consumption, while at the sametime preserving an acceptable signal-to-noise ratio at the input of thedecoding process.

An embodiment of the invention relates to a digital processing devicefor a modulated signal, arranged at the input of a radio frequencyreceiver chain, suited in particular to a transmission system usingbinary carrier phase modulation by means of a binary message on which adirect sequence spread spectrum operation has been carried out, thisdevice comprising analog-to-digital conversion means performingundersampling of the signal received, leading to an at least partialoverlapping of the frequency range of the undersampled wanted signal bythe frequency range of a first interfering signal corresponding to thenoise of the transmission channel, demodulation means connected at theoutput of the analog-to-digital conversion means in order to bring theundersampled wanted signal back to baseband, a low pass filter connectedat the output of the demodulation means and a filter matched to thespreading code used, wherein the analog-to-digital conversion meansinclude a comparator capable of comparing the amplitude of theundersampled signal to a reference value, in order to carry out aquantizing of the 1-bit undersampled signal, said comparator causing thecreation of a second interfering signal corresponding to the quantizingnoise, and including an additional filtering unit arranged between thelow pass filter and the matched filter, said filtering unit implementinga multi-noise, stochastic matched filtering operation making it possibleto improve the overall signal-to-noise ratio, at the input of the filtermatched to the spreading code, taking into account the signal-to-noiseratio of the transmission channel, on the one hand, and thesignal-to-quantizing noise ratio, on the other hand.

According one embodiment, the additional filtering unit includes aplurality Q of finite response base filters mounted in parallel, each ofwhich receives an undersampled signal supplied at the output of the lowpass filter, each filter being characterized by a set of N coefficients,this number N being determined such that it corresponds to the minimumnumber of samples for describing one bit of the spread message, thecoefficients of each of the Q filters corresponding respectively to thecomponents of the Q eigen vectors associated with at least the Qeigenvalues greater than 1 of the matrix B⁻¹A, where A is thevariance-covariance matrix of the wanted signal and B is the meanvariance-covariance matrix of the variance-covariance matrices of thefirst and second interfering signals.

Advantageously, for each filter of the plurality Q of finite responsefilters, the additional filtering unit includes means for multiplyingthe signal obtained at the output of said filter, with, respectively,the central coefficient of the vector resulting from the product betweenthe variance-covariance matrix B and the eigen vector defining thecoefficients of said filter, said unit further comprising means ofsumming up the vectors resulting from all of these operations, supplyinga signal corresponding to the output signal of the reformatted low passfilter having an improved signal-to-noise ratio.

A device according to an embodiment of the invention advantageouslyincludes a comparator installed at the output of the additionalfiltering unit, capable of comparing the amplitude of the output signalsupplied by the summation means to a threshold value and of delivering abinary signal at the output of the filtering unit based on saidcomparison.

The comparator has an adjustable threshold value in one embodiment.

Inserted between the analog-to-digital converter and the demodulationmeans, the device advantageously includes an estimation unit providedfor estimating the center frequency of the signal after undersampling,the signal present at the output of the estimation unit being filteredby a band-pass filter before being applied to the demodulation means, soas to retain only a single spectral motif from amongst the plurality ofspectral motifs representative of the signal after undersampling.

According to one embodiment, the estimation unit includes means fordetermining the parameter N defining the order of the filters of theplurality Q of finite response filters of the additional filtering unit,and for configuring the additional filtering unit using said parameterN.

The sampling frequency corresponds to at least twice the bandwidth ofthe signal transmitted in one embodiment.

According to one embodiment, the filter matched to the spreading code isa digital finite impulse response filter.

BRIEF DESCRIPTION OF THE DRAWINGS

Characteristics and advantages of one or more embodiments of theinvention will become more apparent upon reading the followingdescription given by way of a non-limiting, illustrative example andmade with reference to the appended figures.

FIG. 1 is a schematic illustration of a conventional receiving andprocessing chain for a signal.

FIG. 2 is a schematic illustration of the various functional unitsinvolved in the conventional digital solution of the DSP unit of FIG. 1.

FIG. 3 is a schematic representation of the structure of a finiteresponse filter matched to the spreading code used, implemented in theDSP unit of FIG. 1.

FIG. 4 is a schematic illustration of the design of the DSP unit, withan input comparator, according to an embodiment of the invention.

FIG. 5 shows an embodiment of the additional filtering function at theoutput of the DSP unit demodulation stage (including the low passfilter) according to an embodiment of the invention.

DETAILED DESCRIPTION

An embodiment of the invention thus relates to a receiver device suitedto a transmission system using a direct sequence spread spectrum and ofthe type comprising a digital processing device (DSP) for digitizing andprocessing the signal received at the moment of reception, by means ofundersampling.

This device is designed for receiving and decoding a digital inputsignal E composed of bits each of which, based on its “1” or “0” value,is represented by either of two symbols where each symbol comprises aseries of N symbol elements, distributed over either of two differentlevels. These symbols, for example, may correspond to a Barker code.

These symbol elements are delivered at a predetermined fixed frequency Fcorresponding to a determined period T=1/F, and the N symbol elements ofthe symbol encoding the “1” bit are anti-correlated to the correspondingN symbol elements of the symbol encoding the “0” bit.

In order to be able to preserve the advantages in using a digitalprocessing device, the structure of which was described above withreference to FIGS. 1 and 2, while at the same time reducing theelectrical power consumed and the operating surface occupied by thecomplete circuit, in one embodiment the M-bit ADC 31 of the conventionalsolution is replaced with a comparator-type structure.

Therefore, as indicated in FIG. 4, the DSP unit according to anembodiment of the invention includes a comparator 38 as the input unit,followed by a conventional processing chain up to the demodulation unit(low pass filtering included). The comparator 38 is set to anundersampling frequency and is capable of comparing the amplitude of thesignal E received at the input of the digital processing chain to areference value REF, corresponding to the average value of the highstate and low state of the signal involved. For example, when a NRZ-typecode (non return to zero) is used for the coding, the reference valuewill be assumed to be equal to zero, the high and low states of thesignal being 1 and −1, respectively.

In this way, the input comparator 38 is equivalent to ananalog-to-digital converter using an undersampling of the signalreceived and performing a 1-bit coding of the samples. The number ofnumeric values possible for each discrete value of the signal then beingequal to two, the signal thus quantified will be very far from theoriginal. This quantification error, linked to the use of the inputcomparator 38, thereby causes the creation of an additional disturbancefrom the one related to the transmission channel noise, resulting inconsiderable quantizing noise which may impair the signal. The effect ofthis quantizing noise with respect to the original signal constitutesthe signal-to-quantizing-noise ratio.

A solution adopted, which is based on the input comparator in lieu ofthe M-bit analog-to-digital converter, thus has the effect of adding aquantizing noise that is peculiar to the signal, in addition to thetransmission channel noise.

In addition, taking into account the various noises of the digitalprocessing chain according to an embodiment of the invention, it isappropriate to increase its robustness towards these various noises.Therefore, an embodiment of the invention proposes to add to thestructure of the DSP unit an additional filtering stage provided to bematched to the signal and mismatched to the multiple noises of the chaincomprising the transmission channel noise, on the one hand, and thequantizing noise, on the other hand.

An optimal filter 37 such as this is more precisely provided in order tobe positioned between the low pass filter 35 and the matched filter 36.

The parameter N, necessary to the configuration of the optimal filter37, is estimated in the estimation unit 32 and designates the minimumnumber of samples for describing one bit-time, namely the number ofsamples taken in a period corresponding to the spreading code.Considering the undersampling frequency (Fe) adopted and the bit-timedefined (Tb) upon transmission, this data is readily accessible:

$N = {\frac{T_{b}}{F_{e}} + 1}$

This data is then used to configure the filtering unit 37.

The addition to the DSP unit according to an embodiment of the inventionof this additional filtering stage 37 arranged after the demodulationunit (low pass filtering included), and upstream from the matchedfilter, has the function of impeding the increase in noise power causedby spectrum overlap due to the undersampling operation.

Furthermore, the use of a comparator in lieu of an ADC may produce aserious degradation of the wanted signal by introducing significantquantizing noise. The additional filtering stage 37 therefore also hasthe function of impeding the increase in the quantizing noise powercaused by the use of the comparator 38.

Therefore, using this filter 37 may provide an improvement in thesignal-to-noise ratio after processing in the digital receiver chain, bybeing matched to the wanted signal while at the same time beingmismatched to the various noises. In order to accomplish this, as willbe explained in detail below, the unit 37 is based on a filteringtechnique called multi-noise, stochastic matched filtering.

A filtering technique such as this makes it possible to define a bank ofQ digital filters FLT1 to FLTQ, mounted in parallel, as shown in FIG. 5.As concerns the principle of a stochastic matched filter, if s(t) andb(t) are considered to be two centered random signals, i.e., zeromathematical expectation, and if it is assumed that s(t) is the signaldeemed to be of interest, and that b(t) is the interfering signal with asignal-to-noise ratio defined as being the ratio of the power of s(t)over the power of b(t), then the stochastic matched filtering comprisesa set of several filters, where each filter, when applied to theadditive mixture s(t)+b(t), improves the signal-to-noise ratio of themixture.

The number of filters present in the bank is closely linked to thecumulative power of the various interfering signals (transmissionchannel and quantizing noises) and their order is given by N (valueestimated in the estimation unit 32, as explained above).

In practice, the N-order filters FLT1 to FLTQ are finite impulseresponse filters and their structure is similar to that alreadydescribed with reference to FIG. 3. Each of these filters, namely thefilters FLT1 to FLTQ, receives, in parallel with the others, the signalto be decoded, as it is supplied at the output of the low pass filter35.

Thus, it is appropriate to properly configure the optimal filtering unit37 by selecting, first of all, the respective coefficients of each ofthe finite impulse response filters FLT1 to FLTQ, in a way that makes itpossible to improve the overall signal-to-noise ratio (transmissionchannel and quantizing noises) upstream from the matched filter 36 inthe receiver chain. In order to accomplish this, according to theprinciples of stochastic matched filtering, the coefficients of thesefilters will be determined, on the one hand, based on the use ofstatistical parameters representative of the signal and, on the otherhand, the various noises.

In practice, the coefficients of each filter actually correspond,respectively, to the components of certain eigen vectors, recorded as f₁to f_(q), of the matrix B⁻¹A, where B is the average variance-covariancematrix of the various noises present after demodulation and A is thevariance-covariance matrix of the wanted signal. The matrix B is thusobtained by determining the mathematical average between the covariancematrix of the noise associated with the transmission channel and thatassociated with the quantizing noise. The signals resulting from thefiltering operations with the filters FLT1 to FLTQ are recorded as S*f1to S*fQ.

As a matter of fact, the signal received can be represented by a randomvector whose components correspond, in practical terms, to the samplesof the sampled signal.

Let X be such a random vector with countable embodiments noted as X^(k).The following notations are adopted:

$x = \begin{pmatrix}x_{1} \\x_{2} \\\vdots \\\; \\x_{n}\end{pmatrix}$ $x^{k} = \begin{pmatrix}x_{1}^{k} \\x_{2}^{k} \\\vdots \\\; \\x_{n}^{k}\end{pmatrix}$

From this point of view, the component x_(i) is a random number and thecomponent x_(i) ^(k) is an element of x_(i) with the probability pk. Thecoefficients x_(i) thus correspond to the samples of the sampled signal.

The mathematical expectation of x_(i), noted as E{x_(i)}, is defined asfollows:

${E\left\{ x_{i} \right\}} = {\sum\limits_{k = 0}^{\infty}\;{p_{k}x_{i}^{k}}}$

This definition thus makes it possible to introduce the mathematicalexpectation of such a random vector:

${E\left\{ X \right\}} = \begin{pmatrix}{E\left\{ x_{1} \right\}} \\{E\left\{ x_{2} \right\}} \\\vdots \\{E\left\{ x_{n} \right\}}\end{pmatrix}$

By definition, it is recalled that the variance-covariance matrix of therandom vector X, noted as G, is defined by:

G=E{XX^(T)}; with XX^(T) defining the dyad of the vector X by the vectorX,

Which is also noted as:

$G = \begin{pmatrix}{E\left\{ {x_{1}x_{1}} \right\}} & {E\left\{ {x_{1}x_{2}} \right\}} & {E\left\{ {x_{1}x_{3}} \right\}} & \cdots & {E\left\{ {x_{1}x_{n}} \right\}} \\{E\left\{ {x_{2}x_{1}} \right\}} & {E\left\{ {x_{2}x_{2}} \right\}} & {E\left\{ {x_{2}x_{3}} \right\}} & \cdots & {E\left\{ {x_{2}x_{n}} \right\}} \\{E\left\{ {x_{3}x_{1}} \right\}} & {E\left\{ {x_{3}x_{2}} \right\}} & {E\left\{ {x_{1}x_{3}} \right\}} & \cdots & {E\left\{ {x_{3}x_{n}} \right\}} \\\vdots & \vdots & \vdots & \; & \vdots \\{E\left\{ {x_{n}x_{1}} \right\}} & {E\left\{ {x_{n}x_{2}} \right\}} & {E\left\{ {x_{n}x_{3}} \right\}} & \cdots & {E\left\{ {x_{n}x_{n}} \right\}}\end{pmatrix}$

When the coefficients x_(i) correspond, as is the case here, to thesamples of a stationary random signal, i.e., E{x_(i)x_(j)} depends onlyon (j−i), then it is possible to construct the variance-covariancematrix only from the set of coefficients E{x₁x₁}, E{x₁x₂}, E{x₁x₃}, . .. , E{x₁x_(n)}. In this case, these coefficients correspond to thevalues assumed by the autocorrelation function of the signal observed.

In practice, the calculation of the coefficients of the matrices A andB, respectively, can be performed using the values assumed by theautocorrelation function of the wanted signal, and the transmissionchannel noise and quantizing noise, respectively.

As a matter of fact, the spreading of the original message beingtransmitted will obtain for it certain statistical properties. Inparticular, one realizes that its autocorrelation function correspondsto the deterministic autocorrelation function of the spreading codeused. Advantageously, the autocorrelation function corresponding to thewanted signal is typically identical for a given spreading code,irrespective of the message being transmitted. Thus, when the messagebeing transmitted is always spread with the same code, theautocorrelation function associated with the signal remains fixed, thestatistics of the signal actually being more closely linked to thespreading code used than to the signal itself.

The variance-covariance matrix A can thus be calculated using theautocorrelation function for the wanted signal.

Furthermore, it is also assumed that the transmission channel noise isstationary, i.e., that its statistical characteristics will not varyover time. As a matter of fact, the transmission channel noise can becharacterized, in terms of frequencies, by the bandwidth of the low passfilter 34, of which the cut-off frequency is known. Thus, theautocorrelation function associated with the transmission channel noise,which is determined in a known manner from the spectral density of thetransmission channel noise at the output of the low pass filter 34,remains invariant. An invariant model is thus obtained for theautocorrelation function of the channel transmission noise.

Taking into account the spectral density of the quantizing noise, whichis a constant, the autocorrelation function specific to the quantizingnoise is calculated in the same way.

Using the two thus calculated autocorrelation functions specific to thetransmission channel noise and to the quantizing noise, twovariance-covariance matrices are obtained whose arithmetic mean providesthe mean variance-covariance matrix B of the various noises present.

The dimensions of the matrices A and B are equal to N, corresponding tothe number of samples required to describe a bit-time. The eigenvaluesand eigen vectors of the matrix B⁻¹A can then be calculated.

In fact, the respective coefficients of the N-order filters FLT1 to FLTQcorrespond to the components of the Q eigen vectors associated with atleast the Q eigenvalues greater than 1 of the matrix B⁻¹A.

Mathematically speaking, the coefficients of the filters are the genericcoefficients of the eigen vectors f_(n) defined by the equation havingthe following eigenvalues:

Af_(n)=λ_(n)Bf_(n), where A represents the variance-covariance matrix ofthe wanted signal, and B the mean covariance matrix of the variousnoises resent.

Only the eigen vectors f_(n) associated with the eigenvalues λ_(n)greater than one are retained. It follows then, that if Q eigenvaluesare greater than 1, the filter bank of the multi-noise, stochasticmatched filtering unit will comprise Q filters.

As a matter of fact, all of the eigen vectors of the matrix B⁻¹Aassociated with eigenvalues greater than 1 are representative of thesignal, and all of the eigen vectors of the matrix B⁻¹A associated witheigenvalues lesser than 1 are representative of the various noisespresent. In other words, only the eigen vectors of the matrix B⁻¹Aassociated with eigenvalues greater than 1 improve the overallsignal-to-noise ratio.

Therefore, the signal S at the output of the low pass filter is filteredby the Q filters FLT1 to FLTQ arranged in parallel, the coefficients ofwhich correspond to the components of the N-dimension eigen vectors f₁to f_(q) associated, respectively, with the Q eigenvalues greater than 1of the matrix B⁻¹A. The coefficients S*f_(n), with n falling between 1and Q, thus represent the signal S filtered by the filters FLT1 to FLTQ.

At this stage, the overall signal-to-noise ratio is improved, but theprocessing carried out has greatly deformed the original signal. It maythen be necessary to reconstruct the signal from the signals S*f_(n)with n falling between 1 and Q.

In order to accomplish this, at the output of each filter FLT1 to FLTQ,multiplication means M₁ to M_(Q) enable the signal obtained to bemultiplied by the central coefficient y_(n) of the vector y_(n),obtained from the product between the variance-covariance matrix B ofthe various noises present and the previously defined associated vectorf_(n):

Y_(n)=Bf_(n), this relationship being understood as the product of thematrix B and the vector f_(n), with n falling between 1 and Q.

It is to be noted that there will therefore be as many vectors Y_(n) asfilters FLTQ.

Each of the coefficients S*f_(n) is therefore multiplied by the centralcoefficient y_(n), with n falling between 1 and Q. Summation means P₁ toP_(Q−1) are then provided in order to sum up the vectors resulting fromall of these operations, so as to obtain, at the output, a vector {tildeover (S)} of length N, having the formula:

$\overset{\sim}{S} = {\sum\limits_{n = 1}^{Q}\;{S*f_{n}y_{n}}}$

The signal {tilde over (S)} is thus a reformatted signal having a morefavorable signal-to-noise ratio than the signal S at the input of thedevice, the filters FLT1 to FLTQ being optimal or near optimal in termsof the signal-to-noise ratio.

This signal is then supplied to the input of a comparator COMP in orderto be compared to a threshold value V0, thereby making it possible torecover a binary signal {tilde over (S)}b at the output of thestochastic matched filtering unit. The processing then continues in aconventional manner using the matched filter 35. Advantageously, as aresult of the matched filtering unit, a signal having a much betterquality, in terms of the signal-to-noise ratio, exists at the input ofthe matched filter 36, which typically makes it much easier to selectthe synchronization of the wanted signal in the matched filter 36.

An example of processing information via undersampling and the use of acomparator at the input of a receiver chain is presented hereinbelow. Inthis example the signal to be encoded and transmitted has a bandwidthB=2 MHz. Said signal is encoded by a Barker code of length 11 andmodulated by a carrier frequency of 2.45 GHz.

The encoded signal is modulated and transmitted in the transmissionchannel, then received by an RF antenna and amplified by an LNA. It isrecognized that the signal has experienced the interference from thetransmission channel, which is assumed to have very low correlation(white noise). To be able to observe the effectiveness of adding themulti-noise, stochastic matched filtering unit, the situation will beused in which the signal-to-noise ratio (SNR) of the receiver chain isequal to 0 dB. In this specific example, the conventional digital chainsupplies unsatisfactory results.

The undersampling frequency Fe is fixed as Fe≧4 B=8 MHz. At the outputof the comparator 38, the SNR is equal to −2.31 dB, this strongdegradation of the signal-to-noise ratio being explained by the additionof a strong quantizing noise.

As was seen, the parameters that define the characteristics of thefilters are Q and N, i.e., their number and order, respectively. In ourexample, N is equal to 5; each filter will thus be of the fifth order.The calculations performed according to the principles set forth aboveresult in the assumption that Q is equal to 3, which provides the numberof filters of the fifth order that are used. The filters Y_(n) serveonly to supply the mean coefficient y_(n). The Table below (Tab. 1)supplies the various coefficients of the optimal filter for the f_(n),Y_(n) and y_(n) considered in our example, with n falling between 1 and3.

TABLE 1 Coefficients of the optimal filter with N = 5 and Q = 3. N = 1 N= 2 N = 3 N = 4 N = 5 f1(Q = 1) 0.5899 −0.9174 1.2715 −0.9147 0.5899f2(Q = 2) −0.7892 0.5078 −0.0000 −0.5078 0.7892 f(Q = 3) 0.4360 0.56520.5072 0.5652 0.4360 Y1(Q = 1) 0.1404 −0.2444 y1 = 0.3034 −0.2444 0.1404Y2(Q = 2 −0.5283 0.1636 y2 = 0.000  −0.1636 0.5283 Y3(Q = 3) 0.18590.4969 y3 = 0.5445 0.4969 0.1859

With a configuration of the optimal filter according to the values inTable 1, a significant improvement in the signal-to-noise ratio can beobserved. As a matter of fact, between the output of the low pass filter35 and the output of the multi-noise, stochastic matched filtering unit37, the SNR passes from −2 db to 0.4 db.

Thus, note should be made of the feature of the multi-noise, stochasticmatched filtering unit, which, on average, achieves a gain ofapproximately 2.6 dB, between its input and output, as concerns the SNR,without which the signal might be rendered unusable because of the useof an input comparator in lieu of the ADC, which may seriously degradethe signal-to-noise ratio. To illustrate this effect, the table below(Tab. 2) supplies the SNR at various points along the undersamplingchain with an input comparator and optimal filter, and the number ofresulting bit errors per 1,000 bit-times of the chain. It appears thatthe number of bit errors is sharply reduced with the addition of anoptimal filter, as compared to the conventional solution.

TABLE 2 Simulation per 1,000 bit-times for the multi-noise, stochasticmatched filtering-based receiver chain of FIG. 4. ReceiverPost-Comparator Pre-matched Number of bit SNR SNR filter SNRerrors/1,000 5 dB −1.5 dB 1.4 dB 0 3 dB −1.7 dB 0.9 dB 4 0 dB   −2 dB0.4 dB 205

The addition of the multi-noise, stochastic matched filtering unit thusmakes it possible to limit the influence of the various noises in thereceiver chain and thereby makes it possible to obtain comparableresults, in terms of errors, to those obtained when using theconventional structure with an input ADC.

However, at an equivalent number of bit errors, an advantage of thestructure according to an embodiment of the invention rests on a minimaloccupancy of surface area, in comparison to the conventional structure.As a matter of fact, the use of an M-bit ADC occupies a much largersurface area and may effectively consume more electrical power than asingle comparator. Moreover, the signal is encoded on 1 bit at theoutput of the comparator. It follows that the subsequent stages consistsolely of minimal digital structures (multiplexers in lieu of the M-bitmultipliers).

The digital processing device according to an embodiment of theinvention thus brings about a reduction in the surface area occupied,coupled with a reduction in the electrical power consumed, in comparisonto a conventional approach.

The receiver chain according to an embodiment of the invention (e.g.,the receiver chain of FIG. 4) may be incorporated into a system such asa cell phone or wireless LAN.

From the foregoing it will be appreciated that, although specificembodiments of the invention have been described herein for purposes ofillustration, various modifications may be made without deviating fromthe spirit and scope of the invention.

1. Digital processing device for a modulated signal, arranged at theinput of a radio frequency receiver chain, suited in particular to atransmission system using binary carrier phase modulation by means of abinary message on which a direct sequence spread spectrum operation hasbeen carried out, this device comprising analog-to-digital conversionmeans performing undersampling of the signal received, leading to an atleast partial overlapping of the frequency range of the undersampledwanted signal by the frequency range of a first interfering signalcorresponding to the noise of the transmission channel, and furthercomprising demodulation means connected at the output of theanalog-to-digital conversion means in order to bring the undersampledwanted signal back to baseband, a low pass filter connected at theoutput of the demodulation means and a filter matched to the spreadingcode used, wherein the analog-to-digital conversion means include acomparator capable of comparing the amplitude of the undersampled signalto a reference value, in order to carry out a 1-bit quantizing of theundersampled signal, said comparator causing the creation of a secondinterfering signal corresponding to the quantizing noise, and in that itincludes an additional filtering unit arranged between the low passfilter and the matched filter, said filtering unit implementing amulti-noise, stochastic matched filtering operation making it possibleto improve the overall signal-to-noise ratio, at the input of the filtermatched to a spreading code, taking into account the signal-to-noiseratio of the transmission channel, on the one hand, and thesignal-to-quantizing noise ratio, on the other hand.
 2. Processingdevice as claimed in claim 1, wherein the additional filtering unitincludes a plurality Q of finite response base filters mounted inparallel, each of which receives the undersampled signal supplied at theoutput of the low pass filter, each filter being characterized by a setof N coefficients, this number N being determined such that itcorresponds to the minimum number of samples for describing one bit ofthe spread message, the coefficients of each of the Q filterscorresponding respectively to the components of Q eigen vectorsassociated with at least Q eigen values greater than 1 of the matrixB⁻¹A, where A is a variance-covariance matrix of the wanted signal and Bis a mean variance-covariance matrix of the variance-covariance matricesof the first and second interfering signals.
 3. Processing device asclaimed in claim 2, wherein for each filter of the plurality Q of finiteresponse filters, the additional filtering unit includes means formultiplying the signal obtained at the output of said filter, with,respectively, the central coefficient of the vector resulting from theproduct between the variance-covariance matrix B and the eigen vectordefining the coefficients of said filter, said unit further comprisingmeans of summing up the vectors resulting from all of these operations,supplying a signal corresponding to the output signal of the reformattedlow pass filter having an improved signal-to-noise ratio.
 4. Processingdevice as claimed in claim 3, further comprising a comparator installedat the output of the additional filtering unit, capable of comparing theamplitude of the output signal supplied by the summation means to athreshold value and of delivering a binary signal at the output of thefiltering unit based on said comparison.
 5. Processing device as claimedin claim 4, wherein the comparator has an adjustable threshold value. 6.Processing device as claimed in claim 2, further comprising between theanalog-to-digital converter and the demodulation means an estimationunit provided for estimating the center frequency of the signal afterundersampling, the signal present at the output of the estimation unitbeing filtered by a band-pass filter before being applied to thedemodulation means, so as to retain only a single spectral motif fromamongst the plurality of spectral motifs representative of the signalafter undersampling.
 7. Processing device as claimed in claim 6, whereinthe estimation unit includes means for determining the parameter Ndefining the order of the filters of the plurality Q of finite responsefilters of the additional filtering unit, and for configuring theadditional filtering unit with said parameter N.
 8. Processing device asclaimed in claim 1, wherein the sampling frequency corresponds to atleast twice the bandwidth of the signal transmitted.
 9. Processingdevice as claimed in claim 1, wherein the filter matched to thespreading code is a digital finite impulse response filter.
 10. Areceiver, comprising: an analog-to-digital converter operable to converta modulated analog signal into an under-sampled digital modulatedsignal, the modulated analog signal including a first component having afrequency spectrum spread to a first-component bandwidth according to aspreading code and including a second component, the converter operableto sample the modulated analog signal at a sampling frequency at leasttwice the first-component bandwidth and to introduce into theunder-sampled signal a third component; a demodulator coupled to theanalog-to-digital converter and operable to recover from theunder-sampled signal a demodulated digital signal including the first,second, and third components having respective strengths; an emphasizercoupled to the demodulator and operable to generate a modifieddemodulated digital signal from the demodulated digital signal byincreasing the strength of the first component of the demodulateddigital signal relative to the strengths of the second and thirdcomponents of the demodulated digital signal; and a de-spreader coupledto the emphasizer and operable to generate a digital baseband signalfrom the modified demodulated digital signal and the spreading code. 11.The receiver of claim 10, wherein: the second component of the modulatedanalog signal comprises a channel-noise component; and the thirdcomponent of the under-sampled digital modulated signal comprises aquantization-noise component.
 12. The receiver of claim 10, furthercomprising: an estimator coupled between the converter and thedemodulator and operable to determine a center frequency of theunder-sampled signal; a band-pass filter coupled between the estimatorand the demodulator, having substantially twice the first-componentbandwidth substantially centered about the center frequency, andoperable to generate a filtered under-sampled signal; and wherein thedemodulator includes, an oscillator operable to generate a demodulationsignal having a frequency substantially equal to the center frequency;and a mixer coupled to the oscillator, operable to receive the filteredunder-sampled signal from the band-pass filter, and operable to generatethe demodulated digital signal as a product of the filter under-sampledsignal and the demodulation signal.
 13. The receiver of claim 12,further comprising a low-pass filter coupled between the demodulator andthe emphasizer and having substantially the first-component bandwidth.14. The receiver of claim 10, further comprising: wherein the modifieddemodulated digital signal comprises an amplitude; and a comparatorcoupled to the emphasizer and operable to generate a binary signalhaving a first level if the amplitude of the modified demodulateddigital signal is greater than a threshold and having a second level ifthe amplitude is less than the threshold.
 15. The receiver of claim 10,wherein the emphasizer comprises: a finite-impulse-response filteroperable to generate an intermediate signal from the demodulated digitalsignal; and a multiplier coupled to the filter and operable to generatethe modified demodulated digital signal from a product of theintermediate signal and a predetermined value.
 16. The receiver of claim10, wherein the emphasizer comprises: finite-impulse-response filterseach operable to generate a respective first intermediate signal fromthe demodulated digital signal; multipliers each coupled to a respectivefilter and each operable to generate a respective second intermediatesignal equal to a product of a respective first intermediate signal anda respective predetermined value; and an adder circuit operable togenerate the modified demodulated digital signal from a sum of thesecond intermediate signals.
 17. The receiver of claim 10, wherein: thefirst component of the demodulated digital signal has a symbol rate; andthe emphasizer comprises, a finite-impulse-response filter having anorder related to a quotient of the sampling frequency divided by thesymbol rate and operable to generate an intermediate signal from thedemodulated digital signal, and a multiplier coupled to the filter andoperable to generate the modified demodulated digital signal from aproduct of the intermediate signal and a predetermined value.
 18. Thereceiver of claim 10, wherein the emphasizer comprises: afinite-impulse-response filter having one or more coefficients relatedto an autocorrelation of the spreading code and operable to generate anintermediate signal from the demodulated digital signal; and amultiplier coupled to the filter and operable to generate the modifieddemodulated digital signal from a product of the intermediate signal anda predetermined value.
 19. The receiver of claim 10, wherein theemphasizer comprises: a finite-impulse-response filter having one ormore coefficients related to an autocorrelation of the second componentof the modulated analog signal and to an autocorrelation of the thirdcomponent of the under-sampled modulated digital signal, and operable togenerate an intermediate signal from the demodulated digital signal; anda multiplier coupled to the filter and operable to generate the modifieddemodulated digital signal from a product of the intermediate signal anda predetermined value.
 20. The receiver of claim 10, wherein theemphasizer comprises: a finite-impulse-response filter havingcoefficients related to elements of an eigen vector of a product of avariance-covariance matrix of the spreading code and a transpose of avariance-covariance matrix of a combination of the second component ofthe modulated analog signal and the third component of the under-sampledmodulated digital signal, the eigen vector being associated with aneigen value of the product greater than one, the filter operable togenerate an intermediate signal from the demodulated digital signal; anda multiplier coupled to the filter and operable to generate the modifieddemodulated digital signal from a product of the intermediate signal anda vector value related to a product of the variance-covariance matrix ofthe combination and the eigen vector.
 21. The receiver of claim 10,wherein the emphasizer comprises: a finite-impulse-response filterhaving coefficients respectively equal to elements of an eigen vector ofa product of a variance-covariance matrix of the spreading code and atranspose of a variance-covariance matrix of an average of the secondcomponent of the demodulated analog signal and the third component ofthe under-sampled modulated digital signal, the eigen vector beingassociated with an eigen value of the product greater than one, thefilter operable to generate an intermediate signal from the demodulateddigital signal; and a multiplier coupled to the filter and operable togenerate the modified demodulated digital signal as a vector equal to aproduct of the intermediate signal and a vector value equal to a productof the variance-covariance matrix of the average and the eigen vector.22. The receiver of claim 10, wherein the analog-to-digital converter isoperable to generate the under-sampled modulated digital signal as aone-bit wide signal.
 23. A system, comprising: a receiver, comprising,an analog-to-digital converter operable to convert a modulated analogsignal into an under-sampled digital modulated signal, the modulatedanalog signal including a first component having a frequency spectrumspread to a first-component bandwidth according to a spreading code andincluding a second component, the converter operable to sample themodulated analog signal at a sampling frequency at least twice thefirst-component bandwidth and to introduce into the under-sampled signala third component; a demodulator coupled to the analog-to-digitalconverter and operable to recover from the under-sampled signal ademodulated digital signal including the first, second, and thirdcomponents having respective strengths; an emphasizer coupled to thedemodulator and operable to generate a modified demodulated digitalsignal from the demodulated digital signal by increasing the strength ofthe first component of the demodulated digital signal relative to thestrengths of the second and third components of the demodulated digitalsignal; and a de-spreader coupled to the emphasizer and operable togenerate a digital baseband signal from the modified demodulated digitalsignal and the spreading code.
 24. A method, comprising: receiving amodulated analog signal at a receiver; under sampling the modulatedanalog signal at a sampling frequency to generate an under-sampleddigital modulated signal having a first component, the modulated analogsignal including a second component having a frequency spectrum spreadto a second-component bandwidth according to a spreading code andincluding a third component, the sampling frequency being at least twicethe second-component bandwidth; recovering from the under-sampled signala demodulated digital signal including the first, second, and thirdcomponents having respective strengths; generating a modifieddemodulated digital signal from the demodulated digital signal byreducing the strengths of the first and third components of thedemodulated digital signal relative to the strength of the secondcomponent of the demodulated digital signal; generating a digitalbaseband signal from the modified demodulated digital signal and thespreading code; and outputting the digital baseband signal at an outputof the receiver.
 25. The method of claim 24, further comprising:determining a center frequency of the under-sampled signal; generating afiltered under-sampled signal having substantially twice thesecond-component bandwidth substantially centered about the centerfrequency; and wherein recovering includes, generating a demodulationsignal having a frequency substantially equal to the center frequency,and generating the demodulated digital signal as a product of thefiltered under-sampled signal and the demodulation signal.
 26. Themethod of claim 24, further comprising: limiting a bandwidth of thedemodulated digital signal to substantially the second-componentbandwidth; and generating the modified demodulated digital signal fromthe bandwidth-limited demodulated digital signal.
 27. The method ofclaim 24, further comprising: generating a binary signal having a firstlevel if an amplitude of the modified demodulated digital signal isgreater than a threshold and having a second level if the amplitude isless than the threshold; and wherein generating the digital basebandsignal comprises generating the digital baseband signal from the binarysignal.
 28. The method of claim 24, wherein generating the modifieddemodulated digital signal comprises: generating an intermediate signalfrom the demodulated digital signal with a finite-impulse-responsefilter; and generating the modified demodulated digital signal from aproduct of the intermediate signal and a predetermined value.
 29. Themethod of claim 24, further comprising: receiving the modulated analogsignal from a propagation channel; wherein the third component of thedemodulated analog signal comprises noise from the channel; and whereinthe first component of the under-sampled modulated digital signalcomprises quantization noise related to the sampling.
 30. The method ofclaim 24, wherein generating the modified demodulated digital signalcomprises: generating first intermediate signals from the demodulatedsignal using respective finite-impulse-response filters; generatingsecond intermediate signals by multiplying each of the firstintermediate signals by a respective predetermined value; and generatingthe modified demodulated digital signal by summing together the secondintermediate signals.
 31. The method of claim 24, wherein: the secondcomponent of the demodulated digital signal has a symbol rate; andmodulating the demodulated digital signal comprises, generating anintermediate signal from the demodulated digital signal with afinite-impulse-response filter having an order related to a quotient ofthe sampling frequency divided by the symbol rate, and generating themodified demodulated digital signal by multiplying the intermediatesignal by a predetermined value.
 32. The method of claim 24, whereingenerating the modified demodulated digital signal comprises: generatingan intermediate signal from the demodulated digital signal using afinite-impulse-response filter having one or more coefficients relatedto an autocorrelation of the spreading code; and generating the modifieddemodulated digital signal by multiplying the intermediate signal by apredetermined value.
 33. The method of claim 24, wherein generating themodified demodulated digital signal comprises: generating anintermediate signal from the demodulated digital signal using afinite-impulse-response filter having one or more coefficients relatedto respective autocorrelations of the first component of theunder-sampled modulated digital signal and the third component of themodulated analog signal; and generating the modified demodulated digitalsignal by multiplying the intermediate signal by a predetermined value.34. The method of claim 24 wherein generating the modified demodulateddigital signal comprises: generating an intermediate signal from thedemodulated digital signal using a finite-impulse-response filter havingone or more coefficients related to respective autocorrelations of thefirst component of the under-sampled modulated digital signal and thethird component of the demodulated digital signal; and generating themodified demodulated digital signal by multiplying the intermediatesignal by a predetermined value.
 35. The method of claim 24 whereingenerating the modified demodulated digital signal comprises: generatingan intermediate signal from the demodulated digital signal using afinite-impulse-response filter having coefficients related to elementsof an eigen vector of a product of a variance-covariance matrix of thespreading code and a transpose of a variance-covariance matrix of acombination of the first component of the under-sampled modulateddigital signal and the third component of the modulated analog signal,the eigen vector being associated with an eigen value of the productgreater than one; and generating the modified demodulated digital signalby multiplying the intermediate signal by a vector value related to aproduct of the variance-covariance matrix of the combination and theeigen vector.
 36. The method of claim 24, wherein generating themodified demodulated digital signal comprises: generating anintermediate signal from the demodulated digital signal using afinite-impulse-response filter having coefficients related to elementsof an eigen vector of a product of a variance-covariance matrix of thespreading code and a transpose of a variance-covariance matrix of acombination of the first component of the under-sampled modulateddigital signal and the third component of the modulated digital signal,the eigen vector being associated with an eigen value of the productgreater than one; and generating the modified demodulated digital signalby multiplying the intermediate signal by a vector value related to aproduct of the variance-covariance matrix of the combination and theeigen vector.
 37. The method of claim 24, wherein generating themodified demodulated digital signal comprises: generating anintermediate signal from the demodulated digital signal using afinite-impulse-response filter having coefficients related to elementsof an eigen vector of a product of a variance-covariance matrix of thespreading code and a transpose of a variance-covariance matrix of acombination of the first and third components of the demodulated digitalsignal, the eigen vector being associated with an eigen value of theproduct greater than one; and generating the modified demodulateddigital signal by multiplying the intermediate signal by a vector valuerelated to a product of the variance-covariance matrix of thecombination and the eigen vector.
 38. The method of claim 24, whereingenerating the modified demodulated digital signal comprises: generatingan intermediate signal from the demodulated digital signal using afinite-impulse-response filter having coefficients respectively equal toelements of an eigen vector of a product of a variance-covariance matrixof the spreading code and a transpose of a variance-covariance matrix ofan average of the first component of the under-sampled modulated digitalsignal and the third component of the modulated analog signal, the eigenvector being associated with an eigen value of the product greater thanone; and generating the modified demodulated digital signal as a vectorby multiplying the intermediate signal by a vector value equal to aproduct of the variance-covariance matrix of the average and the eigenvector.
 39. The method of claim 24, wherein under sampling the modulatedanalog signal comprises: comparing the modulated analog signal to athreshold value at the sampling frequency; and generating an amplitudeof the under-sampled digital modulated signal having a first level if anamplitude of the modulated analog signal is greater than the thresholdvalue and having a second level if the amplitude of the modulated analogsignal is less than the threshold value.